dorsal/arxiv
View SchemaOrder Parameter Equations for Front Transitions: Nonuniformly Curved Fronts
| Authors | Aric Hagberg, Ehud Meron |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9707007 |
| URL | https://arxiv.org/abs/patt-sol/9707007 |
| DOI | 10.1016/S0167-2789(98)00143-2 |
Abstract
Kinematic equations for the motion of slowly propagating, weakly curved fronts in bistable media are derived. The equations generalize earlier derivations where algebraic relations between the normal front velocity and its curvature are assumed. Such relations do not capture the dynamics near nonequilibrium Ising-Bloch (NIB) bifurcations, where transitions between counterpropagating Bloch fronts may spontaneously occur. The kinematic equations consist of coupled integro-differential equations for the front curvature and the front velocity, the order parameter associated with the NIB bifurcation. They capture the NIB bifurcation, the instabilities of Ising and Bloch fronts to transverse perturbations, the core structure of a spiral wave, and the dynamic process of spiral wave nucleation.
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"date_created": "2026-03-02T18:00:29.443000Z",
"date_modified": "2026-03-02T18:00:29.443000Z",
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"abstract": "Kinematic equations for the motion of slowly propagating, weakly curved\nfronts in bistable media are derived. The equations generalize earlier\nderivations where algebraic relations between the normal front velocity and its\ncurvature are assumed. Such relations do not capture the dynamics near\nnonequilibrium Ising-Bloch (NIB) bifurcations, where transitions between\ncounterpropagating Bloch fronts may spontaneously occur. The kinematic\nequations consist of coupled integro-differential equations for the front\ncurvature and the front velocity, the order parameter associated with the NIB\nbifurcation. They capture the NIB bifurcation, the instabilities of Ising and\nBloch fronts to transverse perturbations, the core structure of a spiral wave,\nand the dynamic process of spiral wave nucleation.",
"arxiv_id": "patt-sol/9707007",
"authors": [
"Aric Hagberg",
"Ehud Meron"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1016/S0167-2789(98)00143-2",
"title": "Order Parameter Equations for Front Transitions: Nonuniformly Curved Fronts",
"url": "https://arxiv.org/abs/patt-sol/9707007"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "15f978fb-013d-4d14-802f-5633bbaa8b00",
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"type": "Model",
"variant": "snapshot-2026-03-01",
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